Heat Kernel analysis of Syntactic Structures

TL;DR

This paper applies heat kernel methods to analyze syntactic parameter data, revealing structural relations, clustering patterns, and optimal variable choices through low-dimensional embeddings.

Contribution

It introduces a novel application of heat kernel analysis to syntactic data, highlighting connectivity, clustering, and variance structures.

Findings

Identification of syntactic parameter relations

Detection of clustering structures in datasets

Optimal variable regions in parameter space

Abstract

We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin-Niyogi, which produces low dimensional representations of the data, based on Laplace eigenfunctions, that preserve neighborhood information. We analyze the different connectivity and clustering structures that arise in the two datasets, and the regions of maximal variance in the two-parameter space of the Belkin-Niyogi construction, which identify preferable choices of independent variables. We compute clustering coefficients and their variance.